This is what Mathematica calls a pure function. The # represents a variable. #1 is one variable, #2 would be another. In your result, #1 is one new variable Mathematic added. #1^2 is that variable squared. The & is just a sign that the preceding is a pure function.

For example, you could write a function lixe this:

f[x]:= x^2

or you could write it as a pure function:

f=#^2&

Either way, f[3] would give you an answer of 9, and f[x+y] would return (x+y)^2.